Russia · Grade 11 · Practice Sheet 20

1. 1.

   Find the momentum of a 36 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   A cone has base radius 10 cm and height 4 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

   $V = \tfrac{1}{3} \pi r^2 h$

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3. 3.

   Find the force needed to accelerate a 35 kg mass at 6.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A population of 8,300 grows 2% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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5. 5.

   An object has mass 41 g and volume 10 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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6. 6.

   A right-angled triangle has legs of 16 cm and 9 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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7. 7.

   A current of 5.7 A flows through a 35 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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8. 8.

   A wave has frequency 223 Hz and wavelength 3.21 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

   $V = \tfrac{4}{3} \pi r^3$

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10. 10.

    A device runs at 134 V drawing 8.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    An object has mass 258.1 g and volume 29 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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12. 12.

    Find the gravitational potential energy of a 7 kg object raised 18 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 8 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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14. 14.

    Find the force needed to accelerate a 11 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the population standard deviation of: 14, 19, 9, 10, 7 (to 2 d.p.).

    Formula:Standard Deviation (Population)

    $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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16. 16.

    An object has mass 207 g and volume 45 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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17. 17.

    A population of 4,700 grows 10% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

    $N = N_0 (1 + r)^{t}$

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18. 18.

    In a triangle, a = 10, b = 11 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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19. 19.

    Find the sum of the first 3 terms of a geometric series with first term a = 3 and common ratio r = 3.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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20. 20.

    Find the momentum of a 30 kg object moving at 11 m/s.

    Formula:Momentum

    $p = mv$

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